Summing over topologies in non‑perturbative gravitational path integrals

Establish a mathematically controlled prescription for the sum over spacetime topologies in the non‑perturbative gravitational path integral by overcoming the super‑exponential growth of configurations and defining a unique, well‑posed procedure.

Background

The role of topology change in quantum gravity was debated, including whether path integrals should include sums over distinct topologies. Practical and conceptual obstacles were emphasized, particularly the combinatorial explosion of configurations.

It was explicitly noted that there is currently no established, unique way to make sense of summing over topologies in a non‑perturbative gravitational path integral.